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Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...
Learned image features can provide great accuracy in many Computer Vision tasks. However, when the convolution filters used to learn image features are numerous and not separable, feature extraction becomes computationally de- manding and impractical to us ...
Learned image features can provide great accuracy in many Computer Vision tasks. However, when the convolution filters used to learn image features are numerous and not separable, feature extraction becomes computationally demanding and impractical to use ...
We extend results on the dynamical low-rank approximation for the treatment of time-dependent matrices and tensors (Koch and Lubich; see [SIAM J. Matrix Anal. Appl., 29 (2007), pp. 434-454], [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 2360-2375]) to the re ...
Society for Industrial and Applied Mathematics2013
The utilization of the Green's tensor associated with a complex optical background (surface, cavity or stratified medium) leads to a dramatic reduction of the computation effort associated with scattering calculations in that background. This approach is i ...
We investigate the convergence rate of approximations by finite sums of rank-1 tensors of solutions of multiparametric elliptic PDEs. Such PDEs arise, for example, in the parametric, deterministic reformulation of elliptic PDEs with random field inputs, ba ...
Society for Industrial and Applied Mathematics2010
Tensor completion aims to reconstruct a high-dimensional data set with a large fraction of missing entries. The assumption of low-rank structure in the underlying original data allows us to cast the completion problem into an optimization problem restricte ...
The numerical solution of partial differential equations on high-dimensional domains gives rise to computationally challenging linear systems. When using standard discretization techniques, the size of the linear system grows exponentially with the number ...
We consider linear systems A(alpha)x(alpha) - b(alpha) depending on possibly many parameters alpha = (alpha(1), ... , alpha(p)). Solving these systems simultaneously for a standard discretization of the parameter range would require a computational effort ...
Society for Industrial and Applied Mathematics2011
We present an accurate and self-consistent technique for computing the electromagnetic held in scattering structures formed by bodies embedded in a stratified background and extending infinitely in one direction (two-dimensional geometry), With this fully ...
